This report presents the results of research undertaken to study various problems associated with hypervelocity capture of dust particles in aerogel. The primary topics investigated were the properties of shocked aerogel and the requirements for reliable capture of particles on the STARDUST mission. In particular, the viscosity of shocked aerogel has been an open question. The results presented here suggest that the viscosity of aerogel at high impact velocities is negligible, although there remains some uncertainty about lower velocities. The model adopted for viscosity treats the mixture of polymeric silica and decomposition products and finds that, for particle velocities of 6-7 km/s, the viscosity is similar to that typical of light gasses at STP. Expressions for the Hugoniot of aerogel as a function of density were also obtained from the available data. All aerogels of interest for cosmic dust collectors have very similar shock velocity-particle velocity Hugoniot curves. The strength behavior of aerogel for low-speed penetration was measured, but further work is needed to study the proper way to apply this to the issue of terminal deceleration of a dust particle. Preliminary calculations designed to maximize the penetration depths were performed to determine the required density of aerogel to reliably stop a particle in a 3 cm thickness of aerogel (the path length expected for a normal impact into the STARDUST collector). In order to stop a particle of density rho(sub p) and diameter d(sub p), the mean density of the aerogel collector should be no less than that given by the expression bar rho(sub 0) = 1.085 X 10(exp -4 )rho(sub p)d(sub p), for densities measured in g/ cu cm and the particle diameter measured in micrometers.